US 6744825 B1 Abstract A method and system for quadrature modulation and digital-to-analog conversion of a sampled and digitally represented complex baseband signal which permits the use of simple, power-saving, accurate and effective digital signal processing up to a very high intermediate frequency. The invention requires an input signal in the form of an oversampled complex baseband signal. The inphase (I) and quadrature-phase (Q) components of this signal are first quantized to preferably 1 bit per sample, e.g., with the aid of ΣΔ modulation, so that the quantization noise is essentially forced outside the frequency band of the working signal. Then the sampling rate of the quantized versions of I and Q is converted to four times the desired carrier frequency, before the signal is quadrature modulated with a signal frequency exactly equal to one quarter of the final sampling rate. Finally the ready processed digital signal is converted to an analog quadrature modulated signal through a digital-to-analog converter followed by a bandpass filter.
Claims(17) 1. A method of quadrature modulation and digital-to-analog conversion, comprising the steps of:
sampling a digitally represented input complex baseband signal, represented by an in-phase (I) component and a quadrature-phase (Q) component, at a sampling rate to achieve a desired noise shaping;
separately quantizing the in-phase component and the quadrature-phase component to a number of bits per sample to produce quantized versions of the in-phase and quadrature-phase components, the quantizing step introducing quantization noise that is shaped spectrally to have energy falling largely outside the frequency band of the input complex baseband signal;
quadrature modulating the quantized versions of the in-phase and quadrature-phase components to a quadrature modulated signal at a carrier frequency equal to a quadrature modulated signal exactly one quarter of a sampling rate fs to obtain a quadrature modulated signal with repeated spectra of the modulated signal being found around all odd multiples of the carrier frequency;
converting the quadrature modulated signal to an analog form signal through a digital-to-analog converter; and
eliminating unwanted energy outside a frequency band used for a target channel by passing the analog form signal through a bandpass filter wherein,
said quantizing step uses sigma-delta quantization, and
subsequent to said quantizing step and prior to the quadrature modulating step, there is a further step of separately rate-converting the quantized versions of the in-phase and quadrature-phase components by a factor {fraction (
1/2)}M, where M is a selected positive integer, to a sampling rate fs=2fc/(2k−1) by repetition of each quantized sample a total of {fraction (1/2)}M times if M is an even number greater than 2, by no rate-conversion if M=2, and by omission of an in-phase component sample at every second point of time and omission of a quadrature-phase component at all points of time other than every second point of time if M=1, where k is a selected positive integer and fc is the carrier frequency to which the input complex baseband signal is to be modulated.
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the arguments n, n+1, n+2, and n+3 indicating represented points of time.
8. A system for quadrature modulation and digital-to-analog conversion, comprising:
input points of first and second samplers respectively for receiving an in-phase (I) component and a quadrature-phase (Q) component of a baseband signal;
inputs points of first and second quantization units respectively connected to outputs of the first and second samplers, each of the quantization units for separately quantizing the in-phase component and the quadrature-phase component to a number of bits per sample to produce quantized versions of the in-phase and quadrature-phase components, the quantized versions of the in-phase and quadrature-phase components having quantization noise shaped spectrally to have energy falling largely outside the frequency band of the input complex baseband signal;
a modulating device with a modulating device, with modulating channels, comprising an in-phase modulating channel and a quadrature-phase modulating channel,
the modulating channels combining at a common output,
the modulating channels quadrature modulating the quantized versions of the in-phase and quadrature-phase components to a quadrature modulated signal, appearing at the common output, at a carrier frequency equal to exactly one quarter of a sampling rate fs to obtain a quadrature modulated signal with repeated spectra of the modulated signal being found around all odd multiples of the carrier frequency;
a digital-to-analog converter having an input connected to the common output, the converter converting the quadrature modulated signal and, at a converter output, providing an analog form signal; and
a bandpass filter having an input connected to the converter output, the filter to eliminate energy outside a frequency band used by a target channel wherein,
said quantization units are sigma-delta quantization units, and said system further includes separate rate converting units for separately rate-converting the quantized versions of the in-phase and quadrature-phase components by a factor {fraction (
1/2)}M, where M is a selected positive integer, to a sampling rate fs=2/(2K−1) by repetition of each quantized sample a total of {fraction (1/2)}M times if M is an even number greater than 2, by no rate- conversion if M=2, and by omission of an in-phase component sample at every second point of time and omission of a quadrature-phase component at all points of time other than every second point of time if M=1, where k is a selected positive integer and fc is the carrier frequency to which the input complex baseband signal is to be modulated.
9. The system of
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14. The system of
the arguments n, n+1, n+2, and n+3 indicating represented points of time.
15. A system for quadrature modulation and digital-to-analog conversion, comprising:
input points of first and second sampling means respectively for receiving an in-phase (I) component and a quadrature-phase (Q) component of a baseband signal;
first and second quantization means connected to outputs of the first and second sampling means, each of the quantization means for separately quantizing the in-phase component and the quadrature-phase component to a number of bits per sample to produce quantized versions of the in-phase and quadrature-phase components, the quantized versions of the in-phase and quadrature-phase components having quantization noise shaped spectrally to have energy falling largely outside the frequency band of the input complex baseband signal;
a modulating means comprising an in-phase modulating channel means and a quadrature-phase modulating channel means,
the modulating channel means combining at a common output,
the modulating channel means for quadrature modulating the quantized versions of the in-phase and quadrature-phase components to a quadrature modulated signal, appearing at the common output, at a carrier frequency equal to exactly one quarter of a sampling rate fs to obtain a quadrature modulated signal with repeated spectra of the modulated signal being found around all odd multiples of the carrier frequency;
a digital-to-analog converter having an input connected to the common output, the converter converting the quadrature modulated signal and, at a converter output, providing an analog form signal; and
a bandpass filter means having an input connected to the converter output, the filter means for eliminating energy outside a frequency band used by a target channel wherein,
said quantization means are sigma-delta quantization units, and said system further includes separate rate converting units for separately rate-converting the quantized versions of the in-phase and quadrature-phase components by a factor {fraction (
1/2)}M, where M is a selected positive integer, to a sampling rate fs=2fc/(2k−1) by repetition of each quantized sample a total of {fraction (1/2)}M times if M is an even number greater than 2, by no rate- conversion if M=2, and by omission of an in-phase component sample at every second point of time and omission of a quadrature-phase component at all points of time other than every second point of time if M=1, where k is a selected positive integer and fc is the carrier frequency to which the input complex baseband signal is to be modulated.
16. The system of claims
15, wherein said modulating means comprises separate means for separately rate-converting the quantized versions of the in-phase and quadrature-phase components to a sampling rate fs=1ts=4fc/(2k−1) where fc is the carrier frequency to which the input complex baseband signal is to be modulated and k is a selected positive integer.17. The system of
the arguments n, n+1, n+2, and n+3 indicating represented points of time.
Description The present invention relates to a method for quadrature modulation and digital-to-analog conversion, and to a system for quadrature modulation and digital-to-analog conversion. More specifically, the invention relates to an entirely new type of transmitter architecture for the transmission of information-carrying signals based on a digital-to-analog conversion directly on an intermediate frequency. Compared to conventional solutions, the invention will mean considerable simplification of the equipment necessary to achieve a transmitter of this type. The principle is based on quantizing the signal, usually to 1 bit per sample, combined with noise shaping and quadrature modulation with exactly one quarter of the sampling rate used, before the digital-to-analog conversion is carried out at a very high frequency. After analog filtering, a ready modulated signal on a fixed intermediate frequency will be obtained, which subsequently may be very easily mixed down to the desired frequency, if necessary. This requires that the sampling rate used is at least as high as four times the desired frequency. In conventional analog transmitter architectures it is usual to use three steps to modulate a signal to a desired frequency. Once the signal has first been quadrature modulated to a low intermediate frequency, it is mixed up to a high intermediate frequency, before it is finally mixed down to the desired frequency. One of the conventional methods for carrying out digital-to-analog (and analog-to-digital) conversion of a low-pass limited signal (e.g., an audiosignal) is to use ΣΔmodulation of the signal so that it is represented by 1 bit per sample, at the same time as the introduced quantization noise is shaped spectrally so that most of this noise ends up outside the frequency band of interest. To achieve this noise shaping to a sufficient degree, oversampling is used; i.e., a higher sampling rate than is strictly necessary according to Nyquist. One of the major advantages of this technique is that 1 bit sample values can be very easily and accurately converted from digital to analog form (or vice versa). It is also known that an already oversampled signal can be interpolated very easily by a simple repetition of sample values, without this impairing the signal to any significant degree. Note, however, that although due to the oversampling the pass band is almost unaffected by the error made, the repeated spectra may contain more energy than desired. Furthermore, it is common to use two multipliers for performing digital quadrature modulation of a complex baseband signal to a carrier frequency—one multiplier for the in-phase signal (I) and one for the quadrature-phase signal (Q). In the particular instance of the sampling rate used being exactly four times (optionally twice) the desired carrier frequency, all the samples of the carrier frequency signal will have the values 1, −1 or 0, which means that the multipliers can be replaced by simple logic. This is also used in known technology. It is an objective of the present invention to simplify substantially the equipment necessary to obtain a digital quadrature modulator and digital-to-analog converter. This is accomplished by a method of the type mentioned above, the characteristic features of which are set forth in claim The proposed solution is based on performing digital-to-analog conversion of a digitally modulated signal at a very high carrier frequency which is equal to exactly one quarter of the sampling rate through the digital-to-analog converter, optionally succeeded by an analog frequency conversion to the desired frequency if this is different from the digitally represented carrier frequency. The invention provides a method for quadrature modulation of a complex baseband signal represented in digital form to an analog carrier frequency which is directly linked to the sampling rate. This signal can, if so desired, be further converted to another (usually lower) carrier frequency by known analog techniques. It is immaterial for the invention whether the complex baseband signal contains analog or digital information. An appropriately oversampled version of the accurately represented input signal, which is a complex baseband signal represented by the signal components I and Q, is quantized, usually to 1 bit per sample, using one of the known per se methods for shaping the quantization noise, e.g., ΣΔ modulation. The degree of necessary oversampling is determined primarily by the particular order of the noise shaping which is used, in conjunction with the requirements with respect to noise characteristics in the system concerned. Since the input signal has already been oversampled to a considerable degree, the sampling rate for the quantized versions of the signal components I and Q may, if desired, be further increased by a simple repetition of samples. Due to the oversampling, this simple manner of increasing the sampling rate further will have a minimum effect on the signal band—at the same time as the repeated spectra will also be attenuated. If, however, the requirements are more stringent, the errors may easily be corrected. The final version of the baseband signal thus consists of two streams of quantized (typically 1 bit) sample values, where the sampling rate is many times greater than twice the highest frequency which occurs in the signal. When this baseband signal is quadrature modulated, a carrier frequency is used which is equal to exactly one quarter of this sampling rate. If an amplitude equal to 1 is selected for the carrier frequency signal, it can be represented by the values 1, −1 and 0, so that all multiplications are replaced by simple logical operations. But even more important is the fact that the quadrature modulated signal does not now require any increase in the number of bits per sample. Thus, the quadrature modulated signal is represented by the same number (e.g., 1) of bits per sample without any form of further error or noise being introduced by the quadrature modulator. It should also be mentioned that in the quadrature modulation, every second sample of I and every second sample of Q is to be multiplied by 0. This means that the signal components I and Q do not need to be interpolated to 4 times the desired carrier frequency, but only to twice this frequency, and I and Q will each only have to be represented by a sampling rate which is half the rate used for representing the quadrature modulated signal. Finally, the quadrature modulated signal is transmitted through a digital-to-analog converter followed by a bandpass filter. It is important that this filter suppresses to a significant degree all signals outside the frequency band of the working signal, because the noise shaping process introduces a great deal of noise in these ranges. In addition, this filter will reduce the remains of any repeated spectra to a very low level. The invention will be described in more detail below, with reference to the drawings, wherein: FIG. 1 shows digital quadrature modulation to a fixed carrier frequency. The operations performed inside the dotted line represent one example of how the total block operation can be performed. Possible alternative realizations of this total block operation must, however, produce exactly the same output signal sequence for a given set of input signal sequences. FIG. 2 shows a conventional second order ΣΔ modulator. FIG. 3 shows general noise shaped quantization wherein G(z) determines the noise shaping filter H(z)=1−z FIG. 4 shows a typical signal spectrum (the solid line) and noise spectrum (the dotted line) after noise shaped quantization of a low-pass limited signal. FIG. 5 shows the module of the frequency transmission function for an interpolator which repeats each sample M=16 times. FIG. 6 shows an example (M=16) of a signal spectrum (the solid line) and noise spectrum (the dotted line) for a ready interpolated signal I or Q immediately prior to digital quadrature modulation. FIG. 7 shows an example (M=16) of a signal spectrum (the solid line) and a noise spectrum (the dotted line) for f The input signal is a low-pass limited complex baseband signal containing all the information which later is to be modulated onto a fixed intermediate frequency. It is irrelevant what type of information (e.g., analog or digital) is represented by the baseband signal. It is also irrelevant for the invention which type of modulation method is used, and if it is a single or a multi-carrier signal. It may even be a multi-channel signal consisting of a number of individually different channels. In one specific application, the level of the baseband signal can be selected within the range which yields a sufficiently good signal-to-noise ratio in the ready modulated signal. The complex baseband signal is represented by the two real signal components I and Q corresponding to the two branches in the structure in FIG. If, at the outset, the signal components I and Q are not represented by a sufficient degree of oversampling, they must each be interpolated separately to ensure that the sampling rate is sufficiently high before the noise shaped quantizing can be carried out. Conversely, if the input baseband signal is represented by an unnecessarily high degree of oversampling, it may instead first be decimated to the desired sampling rate. Moreover, it must be ensured that the sampling rate of the input signal is an integral factor lower than the desired sampling rate of the quadrature modulated signal which is to be produced. Each signal sample must be represented with sufficient accuracy to ensure that the signal-to-noise ratio in the signal band is better than the application calls for, even at the lowest signal level in question. This is due to the fact that the subsequent signal processing will introduce additional noise. The input signal, represented by samples of the signal components I and Q as described above, are quantized to a number (usually 1) of bits per sample, by using one of the known per se methods for shaping the quantization noise, e.g., ΣΔ modulation. This quantization is carried out on the two signals I and Q, separately, in the units marked NSQ (Noise Shaped Quantization) in FIG. By quantizing the two signal components I and Q (usually to 1 bit per sample), a quantization error will be introduced. This quantization error (or noise) will have a power spectrum that is typically indicated by the dotted line in FIG. The quantized versions of the signal components I and Q should, in principle, each be up-converted separately by a factor M to a sampling rate f Since the signal is subsequently to be quadrature modulated by exactly one quarter of this sampling rate, every second sample of I and every second sample of Q will not be used. Hence it is sufficient to repeat each sample of the quantized versions of the signal components I and Q, separately, ½ M times (instead of M times), as is indicated in FIG. 1, and thereby obtain a sampling rate which is only equal to twice the desired carrier frequency. If M is odd, this means that every second sample is repeated ½(M+1) times and every second sample ½(M−1) times. In fact, the samples of the final versions of the two signal components I and Q should be shifted in time by T=1/f Note that if M=2 a conversion of the sampling rate before quadrature modulation is unnecessary. However, if M=1, the quantized versions of the signal components I and Q must each separately be decimated by 2 (to half the sampling rate). This must be done by having all the original points of time represented, but so that every second point of time is represented by an I sample and the remaining every second point of time by a Q sample. If the equivalent interpolation factor M>1, the simple rate conversion device will in principle perform an up-conversion. The equivalent interpolation filter has the following normalized transmission function, where T=1/f The final versions of the signal components I and Q will automatically be represented by the number of bits per sample which is determined by the quantization device (usually 1 bit per sample). If the oversampling factor of the signal components I and Q at the equivalent sampling rate f If the factor M is an even number (and, in fact, the interpolation is performed by the integer factor ½ M), the final version of the signal components I and Q will always contain an undesired attenuated repeated spectrum centered around f The approximation used in the expression at the far right is very good when F is large, which is the case in the application in question. (Note that even in the case of M=2 and the least conceivable F=2, the error in the approximation is less than 1 dB.) If, e.g., a minimum attenuation of 40 dB of the repeated spectrum centered around f If the factor M is an odd number (and, in fact, every second sample is repeated ½(M+1) times and every second sample ½(M−1) times), the final version of the signal components I and Q will not contain a repeated spectrum centered around f When digital quadrature modulation of I and Q is carried out at a quarter of the sampling rate f or, equivalently where k is an integer. In practice, the digital quadrature modulation can be carried out according to the latter expression by first passing the final versions of the signal components I and Q separately through a modulator, which quite simply inverts every second sample, followed by a multiplexer which retrieves a modulated I-sample and then a modulated Q-sample in alternation. Thus, only every second sample of I and every second sample of Q is in fact used to produce the quadrature modulated signal. This explains why, in practice, there is no need to repeat each sample more than ½M times in the final interpolation (described above), so that the final versions of I and Q each separately are represented by only half of the sampling rate of the quadrature modulated signal. Note that the sampled quadrature modulated signal, which is now actually centered around the carrier frequency f It is important to note that, particularly with respect to implementation, the simple rate conversion device and the digital quadrature modulator, which are enclosed by a dotted line in FIG. 1, are very closely related to each other. Hence these elements of the invention should be regarded as a unity, performing a total operation on the quantized versions of the I and Q signals which is equivalent to interpolating each of the signal components I and Q by , ½M before the quadrature modulation is performed as described above. Given two sample sequences I and Q from the NSQ outputs, possible alternative realizations of the combined operation must produce exactly the same output sequence for the quadrature modulated signal. But the practical realization may be different. The above described realization therefore represents just one specific example of how these operations could be combined. One alternative realization is, of course, to repeat each quantized sample of I and Q (separately) M times in succession to obtain a final sampling rate f The quadrature modulated signal, represented by f Note, however, that for any M>1, the quadrature modulator of this invention will in fact delay the sequence of Q sample values by exactly one sample interval T The quadrature modulated signal, which thus is still represented by a small number (usually 1) of bits per sample, finally passes through a digital-to-analog converter before it is filtered in a bandpass filter. This filter must have sufficient attenuation outside the signal band to ensure that the shaped quantization noise and the rest of the repeated spectra are attenuated to a sufficient degree for the application in question. Patent Citations
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